1. Field of the Invention
The present invention relates to electronics, and, in particular, to transconductance amplifiers.
2. Description of the Related Art
A transconductance amplifier is a type of electrical circuit that transforms an input voltage into an output current. Some transconductance amplifiers convert AC input voltages into AC output currents. There are many applications for which it is desirable that the performance of such a transconductance amplifier be linear. That is, the gain provided by the amplifier is substantially constant over a relatively wide range of input voltage amplitudes and frequencies. Transconductance amplifiers often employ feedback to improve linearity. While feedback can improve linearity, it can also create instability which may lead to undesirable oscillation. Potential instability is manifested as "peaking" in a plot of the closed-loop gain versus frequency response. For many applications, peaking greater than about 3 dB is considered to be unacceptable.
FIG. 1 shows a block diagram of a conventional differential-input transconductance amplifier 100 used to convert a differential AC input voltage (V.sub.IN1P, V.sub.IN1N) into a differential AC output current (I.sub.OUTP, I.sub.OUTN). Amplifier 100 comprises two symmetric half circuits, each half circuit corresponding to a singleinput transconductance amplifier, separated by an impedance device 126 (preferably a resistor). Each half circuit receives one half of the differential input voltage and, in conjunction with the other half circuit and impedance device 126, generates one half of the differential output current.
In particular, current source 102 provides a constant current to node N3. Feedback (provided by feedback device 108) forces the current into input device 104 (preferably a transistor) to be constant and approximately equal to the current provided by current source 102, even if the input voltage V.sub.INP applied to the base (or gate) of input device 104 changes. Feedback device 108 adjusts the base (or gate) voltage of output device 106, which is also preferably a transistor. Adjusting the base (or gate) voltage of output device 106 affects the current through output device 106. The current through output device 106 gets mirrored by output mirror 112 as one half (i.e., I.sub.OUTP) of the differential output current generated by amplifier 100.
The other half circuit of amplifier 100 (i.e., block components 114-124) operate in an analogous fashion, receiving input voltage V.sub.ININ and generating output current I.sub.OUTN.
Since the current through input device 104 is forced by feedback to be constant, even when an AC signal is applied to the base (or gate) of input device 104, the base-emitter (or gate-source) voltage of input device 104 is also constant. This means that there is a fixed DC voltage drop across input device 104, which, in turn, means that the AC component of input voltage V.sub.IN1P is effectively applied directly to node N1. Similarly, for the other half circuit of amplifier 100, the AC component of input voltage V.sub.IN1N is effectively applied directly to node N2. As such, the differential AC input signal is applied across impedance device 126.
As described above, the current 10 through input device 104 is substantially constant. The current .DELTA.I through impedance device 126 is directly proportional to the differential AC input voltage .DELTA.V, as shown in Equation (1) as follows: EQU .DELTA.I=.DELTA.V/Z (1)
where Z is the impedance of device 126. Since the current arriving at node N1 must equal the current leaving node N1, the current through output device 106 is (I.sub.0 -.DELTA.I). This current gets mirrored (and possibly amplified) by output mirror 112 as I.sub.OUTP =k(I.sub.0 -.DELTA.I), where k is the mirror amplification multiplier. Similarly, assuming that the two half circuits of amplifier 100 have the same component characteristics, the current through output device 118 is (I.sub.0 +.DELTA.I), which gets mirrored as I.sub.OUTN =k(I.sub.0 +.DELTA.I) by output mirror 124.
The difference between I.sub.OUTN and I.sub.OUTP is therefore 2k.DELTA.I or, substituting the relation of Equation (1), 2k.DELTA.V/Z. As such, amplifier 100 of FIG. 1 can be used to convert a differential input voltage .DELTA.V into a differential output current, that can then be used for further processing (e.g., as a current or as a voltage). For example, passing this differential current through another impedance device Z' will yield a voltage 2k.DELTA.VZ'/Z, which is directly proportional to the original differential input voltage .DELTA.V.
One of the drawbacks of amplifiers such as amplifier 100 of FIG. 1 is that they may become unstable at high frequencies. The reason for this may be understood by analyzing a simplified, small-signal equivalent circuit of amplifier 100, such as that shown in FIG. 2. In this simplified circuit, resistor R1 and capacitor C1 represent the equivalent impedance at node N1 of FIG. 1. Similarly, resistor R2 and capacitor C2 represent the equivalent impedance at node N3 of FIG. 1, and resistor R3 and capacitor C3 represent the equivalent impedance at node N5 of FIG. 1. The transconductances of input device 104, feedback device 108, and output device 106 of FIG. 1 are represented by gm1, gm2, and GM3, respectively. Since output mirror 112 of FIG. 1 does not affect the feedback loop dynamics except for effects included in R3 and C3, it has been left out of the simplified circuit of FIG. 2.
Using feedback theory, the open-loop gain (defined to be the total gain around the feedback loop) of the circuit can be used to look for potential instabilities. To do this, the feedback loop is broken at an appropriate point and the gain from the input to the output is found. For the simplified circuit of FIG. 2, it is convenient to break the loop at node 4, apply a current as a stimulus, and determine the resulting output current. The open-loop gain is defined to be the ratio of the output current to the input current. The current gain magnitude (in dB) and the phase (in degrees) are plotted as a function of frequency.
If the total phase shift around the loop is equal to 360 degrees at a point where the gain is still greater than unity, oscillation will occur at that frequency. The difference between 360 and the actual phase shift around the loop at the frequency where the gain is unity is known as the phase margin. As phase margin decreases, the previously mentioned peaking will be observed in the closed-loop response. Phase margin of less than 45 degrees is typically undesirable, and, in some application, phase margin of 60 degrees or more may be required. Because negative feedback is employed, a minimum of 180 degrees of phase shift is present. Each pole in the gain response causes the gain to roll off by 20 dB/decade (6 dB/octave), and contributes 90 degrees of additional phase shift. For the simplified circuit of FIG. 2, poles are found at .omega.1=1/(R1C1), .omega.2=1/C2/(gm2+1/R2)!, and .omega.3=1/(R3C3).
Substitution of appropriate values for actual devices reveals that the pole at .omega.1 is at a very high frequency and that the loop response is dominated by the poles at .omega.2 and .omega.3. Simulations of circuits also show that the poles at .omega.2 and .omega.3 may be closely spaced in frequency. This narrow spacing causes potential instabilities. This is illustrated in the open-loop gain and phase response curves shown in FIG. 3 for the uncompensated amplifier. Each pole contributes a total of 90 degrees of phase shift. Since they are spaced closely together, the 180-degree phase shift added by these two poles occurs in a relatively narrow frequency band, and the phase shift around the loop can reach 360 degrees before the gain drops below unity. This can result in poor phase margin and therefore possible oscillations.
One common known solution to this instability problem is to reduce the bandwidth of the amplifier (often called narrowbanding). Adding a capacitor between nodes N3 and N4 in FIG. I will accomplish this narrowbanding compensation.
FIG. 4 shows a block diagram of a differential-input transconductance amplifier 200 to which standard narrowbanding compensation has been added. Amplifier 200 is analogous to amplifier 100 (with block components 202-226 of FIG. 2 corresponding to block components 102-126 of FIG. 1), except that a capacitor C has been added between nodes N3 and N4 to provide compensation. The increased capacitance causes one of the two dominant poles to move to a much lower frequency. This reduces the unity-gain frequency of the open-loop response to a frequency where the phase margin is sufficient to ensure stability.
Adding a capacitor C between nodes N3 and N4 is equivalent to increasing the capacitance C2 in the simplified equivalent circuit of FIG. 2 and reduces the frequency of one of the dominant poles. Increasing the equivalent capacitance of C3 will have a similar narrowbanding compensation effect. Narrowbanding solves the instability problem by moving one of the poles to a much lower frequency as illustrated in the open-loop gain and phase response curves of FIG. 3 for the narrowband-compensated amplifier. With narrowband compensation, the gain is rolled off to below unity at a frequency below the frequency where the phase shift of the second pole takes affect. While this guarantees that the amplifier will not oscillate, it also greatly limits the frequency of operation.
Another possible solution to the stability problem is to reduce the loop gain. This solves the stability problem by reducing the unity-gain frequency of the open-loop response. Since the pole locations do not have to be affected by such a change, the net result is an improvement in phase margin. However, one of the purposes of using feedback in a transconductance amplifier is to improve linearity. The improvement in linearity is a function of the magnitude of the open-loop gain. Increased gain results in improved linearity. Since linearity is important in many applications of transconductance amplifiers, it is undesirable to reduce the open-loop gain even though such a reduction may solve a stability problem.
What is needed is a compensation scheme that addresses the instability problems of an uncompensated amplifier without unreasonably limiting the range of frequencies over which the amplifier will operate linearly.